Question

The diagonals of rectangle ABCD intersect at point Z. DZ = x + 6 and AC = 5x + 3. find the length of AC

Answer 1

Step-by-step explanation:

The diagonals of a rectangle are congruent and the intersecting point is the middle point of both:

Therefore, for this problem DZ ≅ BZ and DB = DZ + BZ. Also DB ≅ AC. Since DZ ≅ BZ

`\begin{gathered} AC=2DZ \\ 5x+3=x+6 \end{gathered}`

Solving for x:

`\begin{gathered} 5x-x=6-3 \\ 4x=3 \\ x=(3)/(4) \end{gathered}`

To find AC we just have to replace x = 3/4 into the expression for its length:

`\begin{gathered} AC=5x+3 \\ AC=5\cdot(3)/(4)+3=(27)/(4)=6.75 \end{gathered}`

Answer:

AC = 6.75